Dark Primordialism Theory: The Cosmic Hydraulic Framework and the Mathematical Foundations of the Continuous Fluid

This paper presents an advanced extension of the Cosmic Hydraulic Framework, formulating a rigorous mechanical foundation for a continuous, incompressible cosmic fluid system. Addressing the fundamental limitations of vacuum-based and abstract coordinate paradigms, the framework introduces the Principle of Total Fullness, eliminating absolute zero and void metrics in favor of continuous adjacent density variations (dx -> 0). We establish five core mechanical arithmetic operations governing pressure accumulation, redistribution, and permanent circulatory flow continuity. Furthermore, quantitative models are developed to resolve complex astrophysical phenomena—such as solar eclipse flux compression and trajectory bending—strictly through localized pressure gradients and fluid resistance, entirely bypassing spacetime curvature and isolated particle-wave dualities. The micro-dynamics are redefined, demonstrating that mass, electric charges, and electromagnetic radiation operate as pressure vortices, differential sinks, and continuous mechanical waves propagating through a singular primordial medium.